Usenet Newsgroups : rec.puzzles Hall of FameThe rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided. Many of these puzzles also appear in Braingle's own collection. 

Title: Cliff Puzzle 8: Squares and Squares and Squares .... From: cliff@watson.ibm.com If you respond to this puzzle, if possible please send me your name, address, affiliation, email address, so I can properly credit you if you provide unique information. PLEASE ALSO directly mail me a copy of your response in addition to any responding you do in the newsgroup. I will assume it is OK to describe your answer in any article or publication I may write in the future, with attribution to you, unless you state otherwise. Thanks, Cliff Pickover * * * 1. What is the smallest square with leading digit 1 which remains a square when the leading 1 is replaced by a 2? In other words, if x**2 = 1.........., is there a y**2 = 2......... ? 2. What is the smallest square with leading digit 1 which remains a square when the leading 1 is replaced by a 2 and also remains a square when the leading digit is replaced by a 3? 3. What is the smallest square with leading digit 1 which remains a square when the leading 1 is replaced by a 2, and also remains a square when the leading digit is replaced by a 3, and also remains a square when the leading digit is replaced by a 4?
Solution